Exploring Structures of Inferential Mechanisms through Simplistic Digital Circuits

TL;DR

This paper proposes a unifying framework for diverse inferential mechanisms by grounding symbolic AI notions in simple logic-gate circuits, treating the circuit as a material substrate for logic-based inference. It identifies four core inference patterns—merge (comprehension), fusion (generalization), contrast (description), and detachment (specification)—and shows how they map onto activation dependencies across propositional and predicate structures. A probabilistic extension through probabilistic logic programming links the circuit-level dynamics to $P(\cdot)$ values, clarifying how dependencies among dependencies can capture complex cognitive tasks. While speculative, the approach offers a compact, mechanistic lens on higher-level cognitive functions and suggests concrete avenues for integrating axioms from probability theory with symbolic rules to reason about uncertainty and learning in a unified formalism.

Abstract

Cognitive studies and artificial intelligence have developed distinct models for various inferential mechanisms (categorization, induction, abduction, causal inference, contrast, merge, ...). Yet, both natural and artificial views on cognition lack apparently a unifying framework. This paper formulates a speculative answer attempting to respond to this gap. To postulate on higher-level activation processes from a material perspective, we consider inferential mechanisms informed by symbolic AI modelling techniques, through the simplistic lenses of electronic circuits based on logic gates. We observe that a logic gate view entails a different treatment of implication and negation compared to standard logic and logic programming. Then, by combinatorial exploration, we identify four main forms of dependencies that can be realized by these inferential circuits. Looking at how these forms are generally used in the context of logic programs, we identify eight common inferential patterns, exposing traditionally distinct inferential mechanisms in an unifying framework. Finally, following a probabilistic interpretation of logic programs, we unveil inner functional dependencies. The paper concludes elaborating in what sense, even if our arguments are mostly informed by symbolic means and digital systems infrastructures, our observations may pinpoint to more generally applicable structures.

Figures (3)

• Figure 1: A simple digital circuit (a single AND port).
• Figure 2: Circuits and generators reproducing the semantics in standard logic of the conditional $p \rightarrow a \wedge b$.
• Figure 3: Duality and complementarity between the inferential mechanisms expressed by logic gate circuits.